Multiply the following complex numbers, marked as blue dots on the graph: $( e^{13\pi i / 12}) \cdot (3)$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius $1$ The second number ( $3$ ) has angle $0$ and radius $3$ The radius of the result will be $1 \cdot 3$ , which is $3$ The angle of the result is $\frac{13}{12}\pi + 0 = \frac{13}{12}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{13}{12}\pi$.